Pseudo-random number sequence output unit, transmitter, receiver, communication system and filter unit, pseudo-random number sequence output method, transmission method, receiving method and filtering method, and data recording medium

ABSTRACT

A transmitter, receiver, and communication system that utilize a pseudo-random number sequence (PRNS) output unit that provides a PRNS of length N. The PRNS output unit generates the PRNS responsive to a number (s) of prescribed positive integers (q x ), a prescribed real impulse constant (r), and a prescribed non-zero real constant (C), where 1&lt;x&lt;s. The PRNS output unit includes an input acceptance section that accepts the number (s) of real number sequence initial values (Y x ), and the number (s) of integer parameters (p x ); and a calculation section that uses the prescribed real impulse constant (r), the prescribed non-zero real constant (C), the real number sequence initial values (Y x ), the integer parameters (p x ), and the prescribed positive integers (q x ) to calculate a recurrence formula that is used to generate a PRNS (z′[y]) of length N, and that outputs the PRNS (z′[y]), where 1&lt;y&lt;N.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] This invention relates to a pseudo-random number sequence outputunit, transmitter, receiver, communication system and filter unit, apseudo-random number sequence output method, transmission method andreceiving method, and a data recording medium.

[0003] This invention particularly relates to an output unit and outputmethod suitable for outputting pseudo-random number sequences usable asthe spreading codes of an asynchronous CDMA (Code Division MultipleAccess) system for satellite, point-to-point, mobile phone and PHS(Personal Handyphone System) communication systems and other land mobilecommunication systems, and in GPS (Global Positioning System) and otherdistance measurement fields; a transmitter, receiver, communicationsystem, filter unit, transmission method, receiving method and filteringmethod using the spreading codes; and a computer-readable data recordingmedium recorded with a program for implementing any of the foregoing.

[0004] 2. Description of the Prior Art

[0005] Spreading codes developed for enabling spread-spectrumcommunication systems and code division multiple telecommunicationinclude M sequences, Kasami sequences and Gold sequences generated by anLFSR (Linear Feedback Shift Register). These spreading code sequenceshave the following two characteristics.

[0006] First, the auto-correlation function of codes has a peak and thecorrelation between different codes (cross-correlation) is near 0. Thisis very similar to the property of white noise.

[0007] Second, when two different spreading codes contained in a codeset are selected and the code set is constituted such that thecross-correlation is near 0 regardless of which are selected, the numberof codes contained in the code set is small relative to the code length.The number of code types is therefore few.

[0008] On the other hand, TDMA (Time Division Multiple Access) and FDMA(Frequency Division Multiple Access) have been known for many years. Theasynchronous CDMA communication system differs from these in its featureof enabling despreading by use of the correlation characteristic of theused codes even without positive signal synchronization. It is thereforesuperior in privacy, secrecy, anti-interference property, anti-jammingproperty and the like.

[0009] Efforts are being made to put CDMA communication into practicaluse. IMT-2000 (International Mobile Telecommunication 2000), anext-generation wireless telecommunication ITU (InternationalTelecommunication Union) standard, has been selected for adoption.

[0010] Recent research shows that the performance of an asynchronousCDMA communication system is determined by inter-code interference noisevariance σ. When pseudo-white noise type spreading codes like Goldsequences or Kasami sequences are used, the interference noise varianceσ is asymptotically equal to (K−1)/3N, where K is the number ofsimultaneously connected users and N is the code length. (M. B. Pursley,“Performance Evaluation for Phased-Coded Spread-Spectrum Multiple-AccessCommunication—Part I: System Analysis,” IEEE Trans. Communication, vol.25 (1977) pp. 795-799.)

[0011] “Asymptotical” here refers to the case where the user number(number of users) K and the code length N have become large.

[0012] The theoretical limit of asynchronous CDMA communication systemperformance has been considered to be σ=(K−1)/3N. It is known, however,that the asymptotic relationship holds because the spreading codes areassumed to be pseudo-white noise.

[0013] Therefore, when the spreading codes are not pseudo-white noise,i.e., when some degree of correlation is present between differentcodes, the theoretical limit of performance can be improved.

[0014] Spreading codes have recently been discovered that have anauto-correlation function whose inter-code interference noise variance σis lower than that when the spreading codes are pseudo-white noise.Specifically, when the auto-correlation function decreases exponentiallywith a code shift of 1 in the manner of Eq. (1), the interference noisedispersion σ is smaller than in the case of pseudo-white noise.

C(l)≈Const.×(−r)^(l) (−1<r<1)   (1)

[0015] In particular, the optimal correlation function (3) is obtainedwhen the real impulse constant r satisfies Eq. (2).

γ≈2−{square root}{square root over (3)}(must be an equality)   (2)

[0016] $\begin{matrix}{\sigma_{optimal} = \frac{\sqrt{3}\left( {K - 1} \right)}{6N}} & (3)\end{matrix}$

[0017] This means that at the same bit error rate the number ofsimultaneously connected users K is 15% greater than the theoreticallimit number of users of an asynchronous CDMA communication system usingpseudo-white noise as the spreading codes. (G. Mazzini, R. Rovatti, G.Setti, “Interference Minimization by Auto-correlation Shaping inAsynchronous DS-CDMA Systems: Chaos-based Spreading is Nearly Optimal,”IEE Electronic Letters, vol. 35, n. 13, Jun. 24, 1999, pp. 1054-1055)

[0018] This paper also points out that a correlation function satisfyingEq. (1) can be approximately modeled by generating chaos spreading codesby piecewise-linear maps of very large partial slope.

[0019] When an attempt is made to generate such spreading sequences witha DSP (Digital Signal Processor) or the like and utilize them in amobile phone system, for example, the following problems arise owing tothe need for high-speed and low power consumption.

[0020] First, owing to the fact that the spreading codes are generatedby piecewise-linear maps of very large slope, accurate results cannot beobtained by DSP implementation or computer calculation because of highdigit dropout. This makes it difficult to construct a physical circuitor device for generating the spreading codes.

[0021] Second, the piecewise-linear maps with the parameter thatdetermines how the correlation function attenuates cannot be freelydesigned with respect to an arbitrary r (−1<r<1).

[0022] Third, the Mazzini et al. paper points out that few types of thepiecewise-linear maps have correlation functions near optimal. It is,however, desirable to have as many types of codes as possible forrealizing a CDMA communication system. Actual configuration of a CDMAcommunication system using the method taught by this paper is thereforedifficult.

[0023] Fourth, in the case of spreading codes generated using a linearshift register, only 0(N) types of codes having a good correlationcharacteristic with respect code length N are available. This is veryfew relative the original number of code types, which is proportional tothe power of 2 O(2^(N)). It is therefore difficult to cope with anincrease in the number of users.

[0024] Fifth, the small key space makes decoding possible with littletime or trouble. Communication security is therefore poor.

[0025] The teachings of this paper offer no remedy for any of these fiveproblems.

[0026] A need has therefore been strongly felt for a technology forovercoming these problems that is capable of generating spreading codesconsisting of pseudo-random number sequences (also called PN(Pseudo-Noise) sequences) suitable for an asynchronous CDMAcommunication system.

[0027] An object of the present invention is to provide a pseudo-randomnumber sequence output unit, transmitter, receiver, communication systemand filter unit, and a pseudo-random number sequence output method,transmission method, receiving method and filtering method that aresuitable for an asynchronous CDMA communication system, and a datarecording medium recorded with a program for implementing any of theforegoing.

SUMMARY OF THE INVENTION

[0028] The invention that achieves this object will now be explained interms of its principle.

[0029] In a first aspect, the present invention provides a pseudo-randomnumber sequence output unit comprising an input acceptance section, acalculation section and an output section, which output unit isresponsive to s (1<s) number of prescribed positive integers q₁, q₂, . .. , q_(s), a prescribed real impulse constant r (−1<r<1), and aprescribed nonzero real constant C for outputting a pseudo-random numbersequence of length N (1<N).

[0030] The input acceptance section accepts input of:

[0031] s (1<s) number of real number sequence initial values Y₁, Y₂, . .. , Y_(s) (−1<Y₁<1, −1<Y₂<1, . . . , −1 Y_(s)<1); and

[0032] s number of integer parameters p₁, P₂, . . . , p_(s) (2≦p₁, 2≦p₂,. . . 2≦p_(s)) for which q₁ mod p₁≠0, q₂ mod p₂≠0. . . , q_(s) modp_(s)≠0 respectively hold with respect to the prescribed positiveintegers q₁, q₂. . . q_(s).

[0033] The calculation section uses the prescribed real impulse constantr, the prescribed non-zero constant C, the sequence initial values Y₁,Y₂, . . . , Y_(s), the integer parameters p₁, p₂, . . . , p_(s), theprescribed positive integers q₁, q₂, . . . , q_(s) and integers j(1≦j≦s), m (1≦m≦2N−2) and n (1≦n≦2N−1) to calculate from the recurrenceformula:

[0034] [T(p,cos theta)-cos(ptheta)=>T(p,cos theta)=cos(p theta)]

T _(p)(cos θ)=T(p, cos θ)−cos(pθ)

y _(j)[1]=Y _(j)

y _(j) [m+1]=T(p _(j) ,y _(j) [m])

[0035] $\begin{matrix}{{z\lbrack n\rbrack} = {\prod\limits_{j = 1}^{s}\quad {T\left( {q_{j},{y_{j}\lbrack n\rbrack}} \right)}}} & (4)\end{matrix}$

[0036] a pseudo-random number sequence z′[1], z′[2], . . . , z′[N] oflength N that satisfies:

[0037] [

sum_{j=1}

{N}=>C

sum_{j=1}

{N}for any z′[j],j=1, . . . N] $\begin{matrix}\begin{matrix}{{{z^{\prime}\lbrack 1\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}\quad {\left( {- r} \right)^{j}{z\lbrack j\rbrack}}}}},} \\{{{z^{\prime}\lbrack 2\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}\quad {\left( {- r} \right)^{j}{z\left\lbrack {j + 1} \right\rbrack}}}}},} \\{{z^{\prime}\lbrack N\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}\quad {\left( {- r} \right)^{j}{{z\left\lbrack {j + N - 1} \right\rbrack}.}}}}}\end{matrix} & (5)\end{matrix}$

[0038] The output section outputs the pseudo-random number sequencez′[1], z′[2], . . . , z′[N].

[0039] The pseudo-random number sequence output unit according to thepresent invention can be constructed so that the sequence initial valuesY₁, Y₂, . . . , Y_(s) satisfy:

y _(k)[2]T(p _(k) ,Y _(k))   (6)

y _(k) [m+1]T(p _(k) ,y _(k) [m])

Y _(k) =y _(k) [N+1]T(p _(k) ,y _(k) [N])

[0040] with respect to an integer k (1≦k≦s) and an integer m (1≦m≦N).

[0041] The pseudo-random number sequence output unit according to thepresent invention can be constructed so that the prescribed real impulseconstant r satisfies:

2−{square root}{square root over (3)}−0.1≦r≦2−{square root}{square rootover (3)}+0.1.   (7)

[0042] The pseudo-random number sequence output unit according to thepresent invention can be constructed so that every prescribed positiveinteger q₁, q₂. . . q_(s) is 1.

[0043] In a second aspect, the present invention provides a transmittercomprising an input acceptance section, the aforesaid pseudo-randomnumber sequence output unit, a spreading section, and a signaltransmitting section.

[0044] The input acceptance section accepts input of a signal fortransmission.

[0045] The output unit outputs a pseudo-random number sequence of lengthN.

[0046] The spreading section uses the output pseudo-random numbersequence of length N as a spreading code to spectrum-spread the signalfor transmission whose input was accepted.

[0047] The signal transmitting section transmits the spectrum-spreadsignal.

[0048] The transmitter of the present invention can further comprise aselecting section and a parameter transmitting section.

[0049] The selecting section selects sequence initial values Y₁, Y₂, . .. , Y_(s) and integer parameters p₁, p₂, . . . p_(s).

[0050] The parameter transmitting section transmits the selectedsequence initial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁,p₂, . . . p_(s).

[0051] The output unit accepts input of the selected sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . p_(s)and outputs a pseudo-random number sequence of length N.

[0052] The transmitter of the present invention can further comprise aparameter receiving section.

[0053] The parameter receiving section receives sequence initial valuesY₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . p_(s).

[0054] The output unit accepts input of the received sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . p_(s)and outputs a pseudo-random number sequence of length N.

[0055] In a third aspect, the present invention provides a receivercomprising a signal receiving section, the aforesaid pseudo-randomnumber sequence output unit, an inverse spreading section and an outputsection.

[0056] The signal receiving section receives a signal.

[0057] The output unit outputs a pseudo-random number sequence of lengthN.

[0058] The inverse spreading section uses the output pseudo-randomnumber sequence of length N as a spreading code to inverselyspectrum-spread the received signal.

[0059] The output section outputs the inversely spectrum-spread signalas a signal for transmission.

[0060] The receiver of the present invention can further comprise aselecting section and a parameter transmitting section.

[0061] The selecting section selects sequence initial values Y₁, Y₂, . .. , Y_(s) and integer parameters p₁, p₂, . . . p_(s).

[0062] The parameter transmitting section transmits the selectedsequence initial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁,p₂, . . . p_(s).

[0063] The output unit accepts input of the selected sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . p_(s)and outputs a pseudo-random number sequence of length N.

[0064] The receiver of the present invention can further comprise aparameter receiving section.

[0065] The parameter receiving section receives sequence initial valuesY₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . p_(s).

[0066] The output unit accepts input of the received sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . p_(s)and outputs a pseudo-random number sequence of length N.

[0067] In a fourth aspect, the present invention provides acommunication system comprising the aforesaid transmitter and receiver.

[0068] The receiver receives sequence initial values Y₁, Y₂, . . . ,Y_(s) and integer parameters p₁, p₂, . . . p_(s) transmitted by thetransmitter.

[0069] The receiver also receives a signal transmitted by thetransmitter.

[0070] In a fifth aspect, the present invention provides a communicationsystem comprising the aforesaid transmitter and receiver.

[0071] The transmitter receives sequence initial values Y₁, Y₂, . . . ,Y_(s) and integer parameters p₁, p₂, . . . p_(s) transmitted by thereceiver.

[0072] The receiver receives a signal transmitted by the transmitter.

[0073] In a sixth aspect, the present invention provides a filter unitcomprising an input terminal, a delay section, an amplifying section, anadder section and an output terminal, which filter unit filtersaccording to a prescribed real impulse constant r (−1<r<1).

[0074] The input terminal accepts input of an input signal of chiplength D.

[0075] The delay section outputs a plurality of signals produced bydelaying the input signal whose input was accepted by 0, D, 2D, 3D, . .. , (N−1)D.

[0076] The amplifying section amplifies the delayed output signals(−r)^((N−T)/D) times, where T is the delay time, and outputs theamplified signals.

[0077] The adder section sums the output amplified signals and outputsthe resulting sum signal.

[0078] The output terminal outputs the output sum signal.

[0079] The delay section, amplifying section and adder section of thefilter of the present invention can be constituted as an ASIC(Application Specific Integrated Circuit), a DSP (Digital SignalProcessor) or an FPGA (Field Programmable Gate Array).

[0080] In a seventh aspect, the present invention provides apseudo-random number sequence output method comprising an inputacceptance step, a calculation step and an output step, which method isresponsive to s (1≦s) number of prescribed positive integers q₁, q₂, . .. , q_(s), a prescribed real impulse constant r (−1<r<1), a prescribednon-zero real constant C for producing a pseudo-random number sequenceof length N (1≦N).

[0081] In the input acceptance step, input is accepted of:

[0082] s (1<s) number of real number sequence initial values Y₁, Y₂, . .. , Y_(s) (−1<Y₁<1, −1<Y₂<1, . . . , −1 Y_(s)<1); and

[0083] s number of integer parameters p₁, P₂, . . . , p_(s) (2≦p₁, 2≦p₂,. . . 2≦p_(s)) for which q₁ mod p₁≠0, q₂ mod p₂≠0. . . , q_(s) modp_(s)≠0 respectively hold with respect to the prescribed positiveintegers q₁, q₂. . . q_(s).

[0084] In the calculation step, the prescribed real impulse constant r,the prescribed nonzero real constant C, the sequence initial values Y₁,Y₂, . . . , Y_(s), the integer parameters p₁, p₂, . . . p_(s), theprescribed positive integers q₁, q₂, . . . , q_(s) and integers j(1≦j≦s), m (1≦m<2N−2) and n (1≦n≦2N−1) are used to calculate from therecurrence Formula (4) a pseudo-random number sequence z′[1], z′[2], . .. , z′[N] of length N that satisfies (5).

[0085] In the output step, the pseudo-random number sequence z′[1],z′[2], . . . , z′[N] is output.

[0086] The pseudo-random number sequence output method according to thepresent invention can be constructed so that the sequence initial valuesY₁, Y₂, . . . , Y_(s) satisfy (6) with respect to an integer k (1≦k≦s)and an integer m (1≦m≦N).

[0087] The pseudo-random number sequence output method according to thepresent invention can be constructed so that the prescribed real impulseconstant r satisfies (7).

[0088] The pseudo-random number sequence output method according to thepresent invention can be constructed so that every prescribed positiveinteger q₁, q₂ . . . q_(s) is 1.

[0089] In an eighth aspect, the present invention provides atransmission method comprising an input acceptance step, an output step,a spreading step and a signal transmitting step.

[0090] In the input acceptance step, input of a signal for transmissionis accepted.

[0091] In the output step, a pseudo-random number sequence of length Nis output by the aforesaid pseudo-random number sequence output method.

[0092] In the spreading step, the output pseudo-random number sequenceof length N is used as a spreading code to spectrum-spread the signalfor transmission whose input was accepted.

[0093] In the signal transmitting step, the spectrum-spread signal istransmitted.

[0094] The transmission method of the present invention can furthercomprise a selecting step and a parameter transmitting step.

[0095] In the selecting step, sequence initial values Y₁, Y₂, . . . ,Y_(s) and integer parameters p₁, p₂, . . . , p_(s) are selected.

[0096] In the parameter transmitting step, the selected sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . ,p_(s) are transmitted.

[0097] In the output step, input of the selected sequence initial valuesY₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . , p_(s) isaccepted and a pseudo-random number sequence of length N is output.

[0098] The transmission method of the present invention can furthercomprise a parameter receiving step.

[0099] In the parameter receiving step, sequence initial values Y₁, Y₂,. . . , Y_(s) and integer parameters p₁, p₂, . . . , p_(s) are received.

[0100] In the output step, input of the received sequence initial valuesY₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . , p_(s) isaccepted and a pseudo-random number sequence of length N is output.

[0101] In a ninth aspect, the present invention provides a receivingmethod comprising a signal receiving step, an output step, an inversespreading step and an output step.

[0102] In the signal receiving step, a signal is received.

[0103] In the output step, a pseudo-random number sequence of length Nis output by the aforesaid pseudo-random number sequence output method.

[0104] In the inverse spreading step, the output pseudo-random numbersequence of length N is used as a spreading code to inverselyspectrum-spread the received signal.

[0105] In the output step, the inversely spectrum-spread signal isoutput as a signal for transmission.

[0106] The receiving method of the present invention can furthercomprise a selecting step and a parameter transmitting step.

[0107] In the selecting step, sequence initial values Y₁, Y₂, . . . ,Y_(s) and integer parameters p₁, p₂, . . . , p_(s) are selected.

[0108] In the parameter transmitting step, the selected sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . ,p_(s) are transmitted.

[0109] In the output step, input of the selected sequence initial valuesY₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . , p_(s) isaccepted and a pseudo-random number sequence of length N is output.

[0110] The receiving method of the present invention can furthercomprise a parameter receiving step.

[0111] In the parameter receiving step, sequence initial values Y₁, Y₂,. . . , Y_(s) and integer parameters p₁, p₂, . . . , p_(s) are received.

[0112] In the output step, input-of the received sequence initial valuesY₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . , p_(s) isaccepted and a pseudo-random number sequence of length N is output.

[0113] In a tenth aspect, the present invention provides a filteringmethod comprising an input step, a delaying step, an amplifying step, asumming step and an output step, which filtering method filtersaccording to a prescribed real impulse constant r (−1<r<1).

[0114] In the input step, input of an input signal of chip length D isaccepted.

[0115] In the delaying step, a plurality of signals produced by delayingthe input signal whose input was accepted by 0, D, 2D, 3D, . . . ,(N−1)D are output.

[0116] In the amplifying step, the delayed output signals are amplified(−r)^((N−T)/D) times, where T is the delay time, and the amplifiedsignals are output.

[0117] In the summing step, the output amplified signals are summed andthe resulting sum signal is output.

[0118] In the output step, the output sum signal is output.

[0119] In the present invention, the sequence initial values Y_(k)(1≦k≦s) can be defined as the periodic points of period N of thedynamical system X_(n+1)=T(p_(k), X_(n)) obtained by chaos mappingT(p_(k), ·). Use of this periodic property eliminates redundantcalculation to enable high-speed pseudo-random number generation.

[0120] A program for implementing the pseudo-random number sequenceoutput unit, transmitter, receiver, filter unit and communicationsystem, and the pseudo-random number sequence output method,transmission method, receiving method and filtering method can berecorded on a computer-readable data recording medium such as a compactdisk, floppy disk, hard disk, magneto-optical disk, digital video disk,magnetic tape or semiconductor memory.

[0121] The processing performed in the aforesaid pseudo-random numbersequence output unit, transmitter, receiver, communication system andfilter unit, and the pseudo-random number sequence output method,transmission method, receiving method and filtering method can beimplemented by running the program recorded on a computer-readable datarecording medium of the present invention on any of various devicesequipped with a memory, processor, output device, communication deviceand the like, including, for example, a mobile terminal device such as ageneral-purpose computer, mobile phone unit, PHS unit or game device, aparallel computer or other data processing system, a DSP (Digital SignalProcessor), or an FPGA (Field Programmable Gate Array).

[0122] The computer-readable data recording medium recorded with aprogram of the present invention can be distributed and marketedindependently of data processing equipment.

[0123] The above and other objects and features of the invention willbecome apparent from the following description made with reference tothe drawings.

BRIEF EXPLANATION OF THE DRAWINGS

[0124]FIG. 1 is a schematic diagram showing the general configuration ofa pseudo-random number sequence output unit according to the presentinvention.

[0125]FIG. 2 is a graph illustrating Chebyshev maps.

[0126]FIG. 3 is a schematic diagram showing the general configuration ofan FIR filter usable in an embodiment of the present invention.

[0127]FIG. 4 is a graph showing the results of bit error rate simulationby the invention and conventional methods.

[0128]FIG. 5 is a graph showing the results of bit error rate simulationby the invention and conventional methods.

[0129]FIG. 6 is a graph showing the results of bit error rate simulationby the invention and conventional methods.

[0130]FIG. 7 is a graph showing the results of bit error rate simulationby the invention and conventional methods.

[0131]FIG. 8 is a flowchart showing the sequence of processing steps ofthe invention pseudo-random number sequence output method.

[0132]FIG. 9 is a schematic diagram showing the general configuration ofa transmitter according to the present invention.

[0133]FIG. 10 is diagram for explaining direct sequence spectrumspreading.

[0134]FIG. 11 is a schematic diagram showing the general configurationof a receiver according to the present invention.

[0135]FIG. 12 is a schematic diagram showing an embodiment of a receiverenabling correlation detection.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0136] Embodiments of the present invention will now be explained. Itshould be noted that the embodiments set out in the following are solelyfor the purpose of illustration and do not limit the scope of thepresent invention. Although a person skilled in the art will be able toadopt embodiments in which some or all elements are replaced withequivalent ones, such embodiments also fall within the scope of theappended claims for patent.

First Embodiment

[0137]FIG. 1 is a schematic diagram (data flow chart) showing thegeneral configuration of a pseudo-random number sequence output unit 101that is a first embodiment of the present invention. Explanation willnow be made with reference to this figure.

[0138] The pseudo-random sequence output unit 101 of this embodiment isequipped with an input acceptance section 102, a calculation section 103and an output section 104. It outputs a pseudo-random number sequence oflength N (1≦N) in response to s (1≦s) number of prescribed positiveintegers q₁, q₂, . . . , q_(s), a prescribed real impulse constant r(−1<r<1) and a prescribed nonzero real constant C.

[0139] The input acceptance section 102 accepts input of the followingsequence initial values and integer parameters:

[0140] s number of real number sequence initial values Y₁, Y₂, . . . ,Y_(s); provided that −1<Y₁<1, −1<Y₂<1, . . . , −1 Y_(s)<1,

[0141] s number of integer parameters p₁, P₂, . . . , p_(s); providedthat 2≦p₁, p₂, . . . 2≦p_(s) and for which q₁ mod p₁≠0, q₂ mod p₂≠0. . ., q_(s) mod p_(s)≠0 respectively hold with respect to the prescribedpositive integers q₁, q₂. . . q_(s).

[0142] The calculation section 103 uses the prescribed real impulseconstant r, the prescribed nonzero real constant C, the sequence initialvalues Y₁, Y₂, . . . , Y_(s) whose input was accepted, the integerparameters p₁, p₂, . . . , p_(s), the prescribed positive integers q₁,q₂, . . . , q_(s) and integers j (1≦j≦s), m (1≦m≦2N−2) and n (1:5n<2N-1)to calculate from the recurrence Formula (4) a pseudo-random numbersequence z′[1], z′[2], . . . , z′[N] of length N that satisfies (5).

[0143] The output section 104 outputs the calculated pseudo-randomnumber sequence z′[1], z′[2], . . . , z′[N].

[0144]FIG. 2 is a graph showing Chebyshev polynomials used by thecalculation section 103. A Chebyshev polynomial can be defined accordingto the cosine function addition theorem as T(a, cos θ)=cos(aθ), whereinteger a represents the order. On the other hand, direct expression byrational polynomials is possible as follows:

[0145] T(0, x)=1

[0146] T(1, x)=x

[0147] T(2, x)=2x²−1

[0148] T(3, x)=4x³−3x

[0149] All Chebyshev polynomials y=T(a, x) are rational maps that mapthe closed interval −-1<=x<=1 to the closed interval −1<=y<=1.

[0150] In FIG. 2, the Chebyshev polynomials of orders 2 to 5 are graphedin the form of y=T(2, x), y=T(3, x), y=T(4, x) and y=T(5, x). Theabscissa is the x-axis and the ordinate is the y-axis.

[0151] The calculation performed by the calculation section 103 can beimplemented by polynomial arithmetic using a computer or by anadder-subtracter and multiplier in combination. It can also beimplemented by floating-point arithmetic with a prescribed degree ofaccuracy assurance or by arithmetic using rational numbers. This will bediscussed later.

[0152] In the case of a computer, sequence initial value and integerparameter input acceptance by the input acceptance section 102 andoutput by the output section 104 can be conducted via registers in thecomputer RAM (Random Access Memory) or CPU (Central Processing Unit),and, in the case of an electronic circuit, by use of latches or thelike.

[0153] Since, as can be seen from the recurrence formula set outearlier, the calculations for determining z′[1], z′[2], . . . , z′[N]are mutually independent, they can be conducted in parallel at N ofmaximum parallelism. As the calculations are expressed by a recurrenceformula, moreover, they can be easily carried out by repeatedcomputation using a program loop.

[0154] The fact that the correlation function of the outputpseudo-random number sequence of length N output by this embodimentbecomes the optimum correlation function is based on the Lebesguespectrum theory evolved within the ergodic theory. This theory isexplained by V. I. Arnold and A. Avez in “Ergodic Problems of ClassicalMechanics” (W. A. Benjamin, New York, 1968).

[0155] The Lebesgue spectrum theory will be explained in the following.

[0156] Assume that sequence X₁, X₂ . . . generated from the dynamicalsystem X_(n+1)=F(X_(n)) is ergodic with respect to the limit densitydistribution function (invariant measure) σ (x) dx on domain M definedby the dynamical system.

[0157] Then, from the inner product <u, v>=∫_(M) u(x) v(x) p(x)dx, aHilbert space L₂ whose naturally normed calculation ||·||is ||V ||²=(v,v) can be considered.

[0158] According to the foregoing paper, an orthonormal basis (8)satisfying a special property for an arbitrary ergodic dynamical systemis uniquely present in this space L₂. This is called the Lebesguespectrum.

{φλ,j}_(λεΛ, jε) J   (8)

[0159] λ here labels the individual Lebesgue spectrum classes and j is alabel designating the class function and j takes a countably infinitenumber of non-negative integers.

[0160] It follows from this definition that the Lebesgue spectrum is anorthonomal system of functions composed of an infinite number offunctions. In the particular case where the label λ can take an infinitenumber of types, (cardinality of Λ), the Lebesgue spectrum is called an“infinite Lebesgue spectrum.”

[0161] A special property possessed by the foregoing Lebesgue spectrumis that it satisfies Eq. 9.

φλ,j oF(x)=φλ,j+1(x)  (9)

(for

λε

,

jε>J)

[0162] In other words, if the function (10) below is given, the otherclass λ Lebesgue spectrum functions of (11) can all be obtained byrepeatedly applying map F(·) defining the dynamical system.

φλ,0   (10)

{φλ,j}j≧1   (11)

[0163] From the assumption that the Lebesgue spectrum constitutes anorthonormal system, it follows that all of these functions (12) areorthogonal to arbitrary other functions (13) of the same class andarbitrary functions (14) of other classes.

φλ,j   (12)

φλ,j^(l)   (13)

φλ′,j^(n)   (14)

[0164] One ergodic dynamic system having an infinite Lebesgue spectrumis the Chebyshev chaotic dynamical system given by the quadratic orhigher order Chebyshev polynomial discussed below. The Chebyshev chaosdynamical system is explained by R. L. Alder and T. J. Rivlin in “Proc.Am. Math. Soc. 15”(1964, p794).

[0165] Assume that function B(x) in L₂ can be expanded in terms of aLebesgue spectrum as in Eq. (15). $\begin{matrix}{{B(x)} = {\sum\limits_{j = 1}^{N}{a_{\lambda,j}{\varphi_{\lambda,j}(x)}}}} & (15)\end{matrix}$

[0166] In this case, it follows from the orthogonality of functions withdifferent Lebesgue spectrum that correlation function (16) is given bythe Lebesgue spectrum expansion coefficients as in (17).

<(B)x), B(F ^(l)(x))>≡<B ₀ ,B ₁   (16)

[0167] $\begin{matrix}{{\langle{B_{0},B_{l}}\rangle} = {\sum\limits_{m = l}^{\infty}{a_{\lambda,m}a_{\lambda,{m - 1}}}}} & (17)\end{matrix}$

[0168] This correlation function is equal to the time-average (18)because of the ergodicity. $\begin{matrix}{\overset{\_}{{B(x)}{B\left( {F^{l}(x)} \right)}} = {\lim\limits_{N\rightarrow\infty}{\sum\limits_{n = 1}^{N}{{B\left( X_{n} \right)}{B\left( X_{n + l} \right)}}}}} & (18)\end{matrix}$

[0169] Here, each X_(n) is generated by recurrence formulaX_(n+1)=F(X_(n)) and the ergodic equality showing this time-average tobe equal to the space-average holds for X₁ on almost everywhere M.

[0170] Here, (19) is assumed.

a _(λm) =C(−r)^(m) (m=0, 1, . . . )   (19)

[0171] When this is substituted into the foregoing equation giving thecorrelation function, (20) is obtained and the correlation functiondecreases exponentially as in (21). $\begin{matrix}{{\langle{B_{0},B_{l}}\rangle} = {{{C^{2}\left( {- r} \right)}^{l}1} - \frac{r^{2N}}{1 - r^{2}}}} & (20)\end{matrix}$

 C(l)≡<B ₀ ,B ₁ >=C′(−r)¹(N→∞)   (21)

[0172] A sequence having a correlation function that exponentially dampsin the form of (−r)¹ relative to a code shift amount 1 can thus befreely generated with respect to an arbitrary r (−1<r<1).

[0173] In particular, as discovered by Mazzini et al. at the same biterror rate the number of theoretical connected users can, in the case ofEq. (2), be increased 15% over the number when the spreading sequencesare defined by random codes (including Gold codes and bulk codes).

[0174] As regards interference noise variance, it suffices if therecurrent approximation behavior of the spreading sequences of (3)becomes as shown by Eq. (1) and Eq. (2). It is therefore adequate toprovide an ergodic dynamic system having a Lebesgue spectrum and afilter designed in the manner of (22) at the foregoing B(x) defined bythe Lebesgue spectrum function of the ergodic dynamic system.

a _(λ,m) =C(−r)^(m) , r=2−{square root}{square root over (3)}(m=0, 1, .. . )   (22)

[0175] The issue at this point is how the ergodic dynamic system F(x)and Lebesgue spectrum (8) can be constructed to be readily realizable.This will now be explained with regard to a configuration utilizingChebyshev maps.

[0176] Consider a second or higher order Chebyshev polynomial T_(p)(p≧2). As mentioned earlier, this Chebyshev polynomial is defined asT_(p)(cos θ)=cos(pθ) and, as indicated by (24), is known to have theorthogonal property with respect to the distribution function (23) onclosed interval M=[−1, 1]. $\begin{matrix}{{{\rho (x)}d\quad x} = \frac{d\quad x}{\pi \sqrt{1 - x^{2}}}} & (23) \\{{\int\limits_{M}{{T_{p}(x)}{T_{q}(x)}{\rho (x)}d\quad x}} = {0\quad \left( {{{for}\quad q} \neq p} \right)}} & (24)\end{matrix}$

[0177] A Hilbert space L₂ can be constituted by these Chebyshevpolynomials and the distribution function. In this case, the Chebyshevpolynomials themselves are orthonormal bases possessing a completeproperty in the Hilbert space L₂.

[0178] The foregoing paper also reports that it is a property of adynamical system given by Chebyshev maps with p>1 to have not onlyergodicity but also still stronger mixing property. The ergodicinvariant measure in this case is given by the density function p(x)that defines the foregoing orthogonality.

[0179] From these properties, the system of functions φ_(q,j)(x) isdefined as in (25).

φ_(q,j)(x)=Y _(qpj)(x) (j≧0, q(mod p)≠0)   (25)

[0180] From the orthogonality of the Chebyshev polynomials themselvesand the relationship of (26), it can be seen that the system offunctions φ_(q,j)(x) is a Hilbert spectrum.

φ_(q,j) oT _(p)(x)   (26)

=T _(qpj) oT _(p)(x)

=T _(qpj+1)(x)

=φ_(q,j+1)(x)

[0181] Therefore, if the filter is designed in the manner of (27),explicit solution of the aforesaid Lebesgue spectrum theory correlationfunction enables configuration of spreading codes for an asynchronousCDMA telecommunication system that have the correlation function of Eq.(1). As explained earlier, this is indicated by Mazzini et al. andenables a 15% increase in number of users under a given bit error rateof an asynchronous CDMA compared to the conventional cases based onordinary random codes. $\begin{matrix}\begin{matrix}{{B(x)} = {\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{\varphi_{q,j}(x)}}}} \\{= {\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{T_{q\quad p^{j}}(x)}}}}\end{matrix} & (27)\end{matrix}$

[0182] Here, (28) and (29) hold and it is noted that they become (30)and (31) for an arbitrary integer m (0≦m≦N−1). $\begin{matrix}\begin{matrix}{{B\left( X_{1} \right)} = {\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{\varphi_{q,j}\left( X_{1} \right)}}}} \\{= {\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{T_{q\quad p^{j}}\left( X_{1} \right)}}}}\end{matrix} & (28) \\{{B\left( X_{1} \right)} = {\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{T_{q}\left( X_{1 + j} \right)}}}} & (29) \\\begin{matrix}{{B\left( X_{m} \right)} = {\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{\varphi_{q,j}\left( X_{m} \right)}}}} \\{= {\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{T_{q\quad p^{j + m - 1}}\left( X_{1} \right)}}}}\end{matrix} & (30) \\{{B\left( X_{m} \right)} = {\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{T_{q}\left( X_{m + j} \right)}}}} & (31)\end{matrix}$

[0183] When q=1, function B(X) becomes T_(q)(x)=x and (32) holds.$\begin{matrix}{{B\left( X_{m} \right)} = {\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}X_{m + j}}}} & (32)\end{matrix}$

[0184] This amounts to multiplying each element of the sequence X_(m+1),X_(m+2), . . . , X_(m+j), . . . , X_(m.N−1), X_(m+N), (0≦m≦N−1) by theconstant given by (−r)^(j) and summing the products.

[0185] This is nothing other than the operation of an FIR filter (FiniteImpulse Response Filter), one of the basic filters used in digitalsignal processing.

[0186] Therefore, the FIR filter calculation of the present inventioncan be readily implemented with existing DSP technology.

[0187]FIG. 3 is a schematic diagram showing the general configuration ofan FIR filter 301 constructed in this manner.

[0188] The FIR filter 301 accepts a Chebysev chaos-type spreading codesequence X₁, X₂, X₃, . . . input at a terminal 305.

[0189] The accepted Chebysev chaos-type spreading code sequence issuccessively delayed and distributed by series-connected delay circuits302. The delay time is the chip length.

[0190] The spreading codes successively appearing between the delaycircuits 302 are amplified by amplifiers 303. As indicated in thedrawing, the amplifications factors are (−r)^(N), (−r)^(N−1),(−r)^(N−2), . . . , (−r)², (−r)¹.

[0191] Here, r is optimally made the real impulse constant defined byEq. (2). Insofar as −1<r<1, however, it can be used to generatespreading codes for an asynchronous CDMA telecommunication system evenif it does not strictly satisfy Eq. (2).

[0192] The signals amplified by the amplifiers 303 are summed by anadder 304 to successively output an optimum chaos-type spreading codesequence Y₁, Y₂, Y₃, . . . .

[0193] When the code sequence is periodic, i.e., when X_(j)=X_(j+N−1),provision of 2N−1 number of numerical values X₁, . . . X_(2N−1) isunnecessary. So long as N number of numerical values X₁, . . . X_(N) areavailable, the periodicity can be utilized to calculate B(X_(m)) for allvalues of m (0≦m≦N). The calculation time can therefore be furthershortened.

[0194] It can be seen that, similarly, the product (33) of the Chebyshevpolynomials is also a complete orthonormal bases on the s-dimensionalcubic [−1, 1]^(s). $\begin{matrix}{{\prod\limits_{j = 1}^{s}{T\left( {p_{j},x_{j}} \right)}} = {{T_{p1}\left( x_{1} \right)}{T_{p2}\left( x_{2} \right)}\quad \cdots \quad {T_{ps}\left( x_{s} \right)}}} & (33)\end{matrix}$

[0195] In the present invention, s number of products (34) arecalculated with respect to s-dimensional real numerical values x₁, x₂, .. . , x_(s) generated from a Chebyshev map dynamical system determinedby s number of integer parameters p₁, p₂, . . . , p_(s) for which q₁ modp₁≠0, q₂ mod p₂≠0. . . , q_(s) mod p_(s)≠0 respectively hold withrespect to s number of prescribed positive integers q₁, q₂ . . . q_(s).

z[m]=T _(q1)(x ₁ [m])T _(q2)(x ₂ [m]) . . . T _(qs)(x _(s) [m])(1≦m≦2N−1)   (34)

[0196] The correlation function of the pseudo-random number spreadingsequence of length N (35) composed of the calculated values z[1], z[2],. . . , z[2N−1] satisfies Eq. (1). $\begin{matrix}\begin{matrix}{{{z^{\prime}\lbrack 1\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\lbrack j\rbrack}}}}},} \\{{{z^{\prime}\lbrack 2\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\left\lbrack {j + 1} \right\rbrack}}}}},} \\\vdots \\{{z^{\prime}\lbrack N\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\left\lbrack {j + N - 1} \right\rbrack}}}}}\end{matrix} & (35)\end{matrix}$

[0197] By defining r as in Eq. (2) and setting the code length Nsufficiently long, therefore, interference noise variance inasynchronous CDMA using spreading codes that are s-dimensionalpseudo-random number sequences generated from a direct product chaosdynamical system can, in accordance with the foregoing theory of Mazziniet al., be represented by (3) to increase the number of users at thesame bit error rate reliably by 15% relative to the case of an existingasynchronous CDMA communication system.

[0198] If the topologically conjugacy relationship of (36) is satisfiedwith respect to a Chebyshev map T_(p)(x) and a diffeomorphism G(x),moreover, this F_(p)(x) will also have the same Lebesgue spectrum as theChebyshev map and, in addition, the auto-correlation function cansimilar construct chaos sequences that damp in the manner of (−r)⁻¹.

F _(p) oG(x)=GoT _(p)(x)   (36)

[0199]FIGS. 4 and 5 show simulation results obtained when thepseudo-random number sequence length N was fixed to 31 and bit errorrate was calculated as a function of number of users for each of thepresent method, white noise codes and Gold codes. The followingparameters were used in the present method.

[0200] ·s=1

[0201] ·p=2 (corresponding to a Chebyshev generator order of 2).[<−modified]

[0202] The simulation results demonstrate that at the same bit errorrate the present method enables a 15% increase in number of users overthat in the case of the white noise codes and Gold codes which had beenconsidered to be the optimum existing sequences.

[0203] More specifically, 28 users can communicate with bit error rate0.023 when the present Filter method is employed, while only 25 userscan communicate with the same bit error rate 0.023 when the conventionalspreading sequences are employed.

[0204]FIGS. 6 and 7 show simulation results obtained when thepseudo-random number sequence length N was fixed to 127 and bit errorrate was calculated as a function of number of users for each of thepresent method, white noise codes and Gold codes. The followingparameters were used in the present method.

[0205] ·s=1

[0206] ·p=2 (corresponding to a Chebyshev generator order of 2)

[0207] The simulation results demonstrate that at the same bit errorrate the present method enables a 15% increase in number of users overthat in the case of the white noise codes and Gold codes which had beenconsidered to be the optimum existing sequences.

[0208] More specifically, 115 users can communicate with bit error rate0.025 when the present Filter method is employed, while only 100 userscan communicate with the same bit error rate 0.025 when the conventionalspreading sequences are employed.

[0209] Such simulation results as shown in FIGS. 4 to 7 are very robustunder the finite precision effect of digital computers. This finding isto be published in a paper reporting the joint work of four researchersincluding the inventor: C. C. Chen, K. Yao, K. Umeno, E. Biglieri“Applications of Chaotic Dynamical Systems and Ergodic Theory to theDesign of Spread Spectrum Sequences” (preprint submitted to IEEE trans.on Circuits and Systems. Submission date: Jan 31, 2000).

[0210] This embodiment thus overcomes the five problems explainedearlier.

[0211]FIG. 8 is a flowchart showing the sequence of processing stepsexecuted by the pseudo-random sequence output unit 101, i.e., theprocessing of the invention pseudo-random number sequence output method.

[0212] The pseudo-random sequence output unit 101 accepts the sequenceinitial values and integer parameters (orders) (step S301), uses themand the aforesaid recurrence formula to calculate a pseudo-random numbersequence (step S301), and outputs the calculated pseudo-random numbersequence (step S303) to complete the processing.

[0213] The pseudo-random number sequence output method of the presentinvention can thus be readily implemented with a general-purposecomputer, parallel computer, mobile terminal (particularly atelecommunication terminal), game device or other such data processingsystem.

[0214] The pseudo-random number sequence output method of the presentinvention can also be readily implemented with a DSP, FPGA (FieldProgrammable Gate Array) or other such digital processing circuit.

Embodiment of Transmitter

[0215]FIG. 9 is a schematic diagram showing the general configuration ofa transmitter 401 according to the present invention. Elements similarto those in the foregoing figures are assigned like reference symbols.Explanation will now be made with reference to FIG. 9.

[0216] The transmitter 401 comprises a signal acceptance section 402,sequence output section 403, a spreading section 404 and a signaltransmitting section 405. The sequence output section 403 is equippedwith the pseudo-random sequence output unit 101, which it controls.

[0217] The signal acceptance section 402 accepts the signal to betransmitted. In the case of a mobile phone or PHS, the signal fortransmission is typically a voice signal. In the case of digitaltelecommunication, it is an electric digital signal. In the case ofoptical telecommunication, the optical signal can be converted to anelectric signal and the electric signal accepted. Or, if thepseudo-random sequence output unit 101 is implemented as an opticalcomputer, the optical signal can be accepted as it is.

[0218] The sequence output section 403 causes the pseudo-random sequenceoutput unit 101 provided therein to accept sequence initial values andinteger parameters (orders) assigned to the transmitter 401. Thepseudo-random sequence output unit 101 produces pseudo-random numbersequences as explained earlier and the sequence output section 403outputs them.

[0219] Different transmitters 401 can in advance be assigned sequenceinitial values and integer parameters (orders) of different values. Manycommunication terminals store a production serial number, productnumber, approval number and the like in a ROM (Read Only Memory). Thesequence initial values and integer parameters (orders) can similarly bestored in a ROM beforehand so that the transmitter 401 can use the samesequence initial values and integer parameters (orders) at all times.Another possible method is to store multiple types of sequence initialvalues and integer parameters (orders) in the ROM and randomly selectthe ones to be used at the time of each communication.

[0220] In the case of such an embodiment, the receiver communicatingwith the transmitter 401 must somehow be informed of the sequenceinitial values and integer parameters (orders) stored in the ROM. Whenthe transmitter and the receiver are paired, they can be embodied to usethe same sequence initial values and integer parameters (orders).

[0221] When multiple types of sequence initial values and integerparameters (orders) are provided, the ones used by the transmitter 401can be determined by correlation detection as explained later. It isalso possible to prepare the sequence initial values using chaos randomnumber sequences obtained by use of a recurrence formula based onChebyshev polynomials. In addition, as explained later, public keyencryption can be used to secure sharing of sequence initial values andinteger parameters (orders) between the transmitter 401 and thereceiver.

[0222] The spreading section 404 effects direct spectrum spreading bysuccessively multiplying the signal for transmission accepted by thesignal acceptance section 402 by the elements of the pseudo-randomnumber sequences output by the sequence output section 403. A methodwill be explained here in which the value of the signal at time t isdefined as s(t) and the signal s(t) is successively multiplied by thesequence elements.

[0223] When the elements of a sequence of length N are used, the periodof “successive multiplication of the signal s(t) by the sequenceelements” resulting from these elements and the chip length w is Nw.

[0224] When “signal s(t) is successively multiplied by the sequenceelements” starting from a prescribed time to, the signal s(t) isdiscretized by chip length w so as to obtain the required quality.Conceivable techniques for this include, for instance, that of obtaininga value of signal s(t) for each chip length w and that of obtaining theaverage value of signal s(t) during chip length w. In the interest ofclarity, the former method will be explained here.

[0225] The chip length w must be long enough to enable the receiver todecode the information of the signal for transmission sufficiently atthe required quality. An appropriate chip length can be selected by aconventional method.

[0226] If an appropriate chip length w is selected, a signal that is notso degraded compared to the original signal for transmission can beobtained by successively outputting the discretized signal sequence forthe selected chip length time W.

[0227] The discretized signal can be expressed by a number sequence suchas the following.

s(t ₀), s(t _(0+w)), s(t _(0+2w)), s(t _(0+3w)), s(t _(0+4w)), . . . .

[0228] This can expressed with regard to integer i (0≦i) assi=s(t_(0+iw)).

[0229] In the method that takes the average value of signal s(t) duringchip length w, the following expression is possible.s₁ = (1/w)∫₀^(w)s(t₀ + i  u)  u

[0230] The signals si (0≦i) are ones obtained by discretizing the signalfor transmission at the required quality.

[0231] The signal sequence after direct spectrum spreading of thissignal sequence is

s ₀ z′[1], s ₁z′[2], . . . , s _(N−1) z′[N], s _(N) z′[1], s _(N+1) z′[²], . . . .

[0232] In other words, the general term of this number sequence withrespect to integer i (0≦i) is s_(i)×z′[(imodN)+1]. x mod y means theremainder when x is divided by y.

[0233] Transmission of the elements of this signal sequence for the timeof each chip length enables transmission of an accepted signal fortransmission of prescribed time length in the same time length.

[0234]FIG. 10 illustrates direct spectrum spreading. The signal fortransmission 501 accepted by the signal acceptance section 402 isrepeatedly multiplied by the elements of the pseudo-random numbersequence 502 output by the sequence output section 403 to produce thesignal 503 output by the spreading section 404.

[0235] The signal transmitting section 405 transmits the signal 503output by the spreading section 404. The transmission is, for example,conducted via an antenna in the case of a mobile phone or PHS, via awire telephone line or wire/wireless LAN in the case of a computernetwork, or via an optical cable.

Embodiment of Receiver

[0236] Like the transmitter, the receiver of the present invention usesthe pseudo-random number sequence output unit to produce pseudo-randomnumber sequences. In the receiver, these pseudo-random number sequencesare used as spreading codes for inverse direct spectrum spreading. FIG.11 is a schematic diagram showing the general configuration of areceiver 601 according to the present invention. Explanation will now bemade with reference to FIG. 11.

[0237] The receiver 601 is equipped with a signal receiving section 602,a sequence output section 604 and an inverse spreading section 605.

[0238] The signal receiving section 602 receives the signal transmittedby the transmitter 401. The signal receiving section 602 is constitutedas an interface with, for example, an antenna, telephone line, opticalfiber line or the like.

[0239] The signal received by the signal receiving section 602 includesthe signal transmitted by the transmitting party's transmitter 401 andnoise. In order to eliminate unneeded signals, the receiver 601 usespseudo-random number sequences that are identical to the pseudo-randomnumber sequences used by the transmitter 401 for direct spectrumspreading. The sequence output section 604 causes the pseudo-randomsequence output unit 101 to accept the sequence initial values andinteger parameters (orders) used by the transmitting party's transmitter401, thereby enabling it to output the pseudo-random number sequences.The sequence output section 604 of the receiver 601 in this embodimentis therefore identical to the sequence output section 403 of thetransmitter 401.

[0240] The signal for transmission accepted by the transmitting party'stransmitter 401 can be despread by inverse direct spectrum spreading thesignal transmitted by the transmitting party's transmitter 401, i.e., bysuccessively multiplying it by the same pseudo-random number sequenceelements. If synchronization has been established, successivemultiplication of the received signal sequence s₀z′[1], s₁z′[2], . . . ,s_(N−1)z′[N], s_(N)z′[1], s_(N+1)z′[2], . . . by the pseudo-randomnumber sequence element z′[1], z′[2], . . . , z′[N] produces the decodedinformation of the signal for transmission at the required quality inthe form of the signal sequence S₀, S₁, . . . , S_(N−1), S_(N), S_(N+1).. . .

[0241] Synchronization can be achieved by the correlation detectionmentioned earlier or by clock sharing or any of various other methods,all of which are encompassed by the present invention.

[0242] As explained below, utilization of public-key encryption in thetransmitter 401 and receiver 601 enables a generator section 611 (FIG.12) of the receiver to generate the same sequence initial values andinteger parameters (orders) as the transmitter 401.

[0243] First, the receiver 601 generates a public key and a private key.The receiver 601 then transmits the public key to the transmitter 401.The transmitter 401 uses the public key to encrypt the sequence initialvalues and integer parameters (orders) it uses and transmits encryptedvalues and parameters (orders) to the receiver 601. The receiver 601uses the private key to decrypt the received encrypted signal and thusobtain the sequence initial values and the integer parameters (orders).

[0244] The chaotic key distribution method taught by the inventor'sJapanese Patent Application No. 11-152063 can be used as the public-keyencryption method.

Embodiment for Correlation Detection

[0245] When the transmitter 401 effects direct spectrum spreading usinga selected one of multiple pseudo-random number sequences, the receiver601 can discriminate the selected pseudo-random number sequence bycorrelation detection. It can also use correlation detection for inversedirect spectrum spreading synchronization.

[0246] An embodiment of the invention receiver capable of correlationdetection will now be explained with reference to FIG. 12. Elements inFIG. 12 similar to those in the foregoing figures are assigned likereference symbols.

[0247] In addition to having the signal receiving section 602, sequenceoutput section 604 and inverse spreading section 605, the receiver 601of FIG. 12 is further equipped with a generating section 611 and acorrelation detecting section 612.

[0248] The generating section 611 outputs sets of sequence initialvalues and integer parameters (orders) selectable by the transmitter401. Output of a single pseudo-random number sequence is alsoacceptable. In this case, owing to the need to select one set from amongmultiple sets of sequence initial values and integer parameters(orders), the correlation detecting section 612 functions to synchronizethe signals.

[0249] In response to the sequence initial values and integer parameters(orders) generated by the generating section 611, the sequence outputsection 604 outputs every pseudo-random number sequence selectable bythe transmitter 401.

[0250] The correlation detecting section 612 attempts correlationdetection with respect to every pseudo-random number sequence output bythe sequence output section 604. Correlation detection is carried out bysuccessively multiplying the received signal by “elements” of thepseudo-random number sequence to be checked. The correlation detectioncan be done using a conventional technique known to the art.

[0251] The pseudo-random number sequences used in the present inventionare excellent in correlation characteristic. When the receiver 601selects a different pseudo-random number sequence, therefore, thestrength of the signal after multiplication is extremely weak and thecorrelation detection fails.

[0252] On the other hand, when the same pseudo-random number sequence asthat of the transmitter 401 is selected and correlation detection isconducted, the strength of the signal after multiplication exceeds aprescribed value. In addition, signal synchronization can be achieved byshifting the pseudo-random number sequence offset to synchronize withthe received signal.

[0253] The inverse spreading section 605 despreads the signal fortransmission by successively multiplying the signal received by thesignal receiving section 602 by the reciprocals of the elements of thepseudo-random number sequence that the correlation detecting section 612has selected and synchronized with the received signal.

[0254] Unlike the correlation detecting section 612, which successivelymultiplies the received signal by the “elements” of the pseudo-randomnumber sequence, the inverse spreading section 605 successivelymultiplies the received signal by the “reciprocals of the elements” ofthe pseudo-random number sequence. Thus the correlation detectingsection 612 calculates correlation/cross-correlation, while the inversespreading section 605 carries out dispreading.

Embodiment of Communication System

[0255] The communication system of the present invention can beconfigured from the transmitter 401 and the receiver 601, which receivesthe signal transmitted by the transmitter 401 and despreads the signalfor transmission. Despreading of the signal for transmission fails whenthe transmitter 401 and receiver 601 use different pseudo-random numbersequences.

[0256] Therefore, even when multiple transmitters 401 and receivers 601communicate on the same frequency band, intercommunication can beconducted while preserving privacy and also assuring communicationquality commensurate with the number of users.

[0257] The pseudo-random number sequences generated according to thepresent invention are particularly advantageous in that they enable agreater stepwise increase in the number of code types than possible withconventional pseudo-random number sequences and, as such, are highlysuitable for CDMA communication including a large number of latentusers.

[0258] As explained in the foregoing, the present invention provides apseudo-random number sequence output unit, transmitter, receiver,communication system and filter unit, and a pseudo-random numbersequence output method, transmission method, receiving method andfiltering method that are suitable for an asynchronous CDMAcommunication system, and a data recording medium recorded with aprogram for implementing any of the foregoing.

What is claimed is:
 1. A pseudo-random number sequence output unitresponsive to s (1<s) number of prescribed positive integers q₁, q₂, . .. , q_(s), a prescribed real impulse constant r (−1<r<1), a prescribednon-zero real constant C for outputting a pseudo-random number sequenceof length N (1≦N), which output unit comprises: an input acceptancesection that accepts input of s (1<s) number of real number sequenceinitial values Y₁, Y₂, . . . , Y_(s) (−1<Y₁<1, −1<Y₂<1, . . . , −1Y_(s)<1), and s number of integer parameters p₁, p₂, . . . , p_(s)(2≦p₁, 2≦p₂, . . . 2≦p_(s)) for which q₁ mod p₁≠0, q₂ mod p₂≠0. . . ,q_(s) mod p_(s)≠0 respectively hold with respect to the prescribedpositive integers q₁, q₂. . . q_(s); a calculation section that uses theprescribed real impulse constant r, the prescribed non-zero realconstant C, the sequence initial values Y₁, Y₂, . . . , Y_(s), theinteger parameters p₁, p₂, . . . , p_(s), the prescribed positiveintegers q₁, q₂, . . . , q_(s) and integers j (1≦j≦s), m (1≦m≦2N−2) andn (1≦n≦2N−1) to calculate from the recurrence formula T _(p)(cos θ)=T(p,cos θ)−cos(pθ) y _(j)[1]=Y _(j) y _(j) [m+1]=T(p _(j) ,y _(j) [m])${z\lbrack n\rbrack} = {\prod\limits_{j = 1}^{s}{T\left( {q_{j},{y_{j}\lbrack n\rbrack}} \right)}}$

a pseudo-random number sequence z′[1], z′[2], . . . , z′[N] of length Nthat satisfies $\begin{matrix}{{{z^{\prime}\lbrack 1\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\lbrack j\rbrack}}}}},} \\{{{z^{\prime}\lbrack 2\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\left\lbrack {j + 1} \right\rbrack}}}}},} \\\vdots \\{{{{z^{\prime}\lbrack N\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\left\lbrack {j + N - 1} \right\rbrack}}}}};}\quad}\end{matrix}$

an output section that outputs the pseudo-random number sequence z′[1],z′[2], . . . , z′[N].
 2. The output unit according to claim 1, whereinthe sequence initial values Y₁, Y₂, . . . , Y_(s) satisfy y _(k)[2]T(p_(k) ,Y _(k)) y _(k) [m+1]T(p _(k) ,y _(k) [m]) Y _(k) =y _(k) [N+1]T(p_(k) ,y _(k) [N]) with respect to an integer k (1≦k≦s) and an integer m(1≦m≦N).
 3. The output unit according to claim 1 or 2, wherein theprescribed real impulse constant r satisfies 2−{square root}{square rootover (3)}−0.1≦r≦2−{square root}{square root over (3)}+0.1.
 4. The outputunit according to any of claims 1 to 3, wherein every prescribedpositive integer q₁, q₂. . . q_(s) is
 1. 5. A transmitter comprising: aninput acceptance section that accepts a signal for transmission; anoutput unit of any of claims 1 to 4 that outputs a pseudo-random numbersequence of length N; a spreading section that uses the outputpseudo-random number sequence of length N as a spreading code tospectrum-spread the signal for transmission whose input was accepted;and a signal transmitting section that transmits the spectrum-spreadsignal.
 6. The transmitter according to claim 5, further comprising: aselecting section that selects sequence initial values Y₁, Y₂, . . . ,Y_(s) and integer parameters p₁, p₂, . . . , p_(s); and a parametertransmitting section that transmits the selected sequence initial valuesY₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . , p_(s); theoutput unit accepting input of the selected sequence initial values Y₁,Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . , p_(s) andoutputting a pseudo-random number sequence of length N.
 7. Thetransmitter according to claim 5, further comprising: a parameterreceiving section that receives sequence initial values Y₁, Y₂, . . . ,Y_(s) and integer parameters p₁, p₂, . . . , p_(s); the output unitaccepting input of the received sequence initial values Y₁, Y₂, . . . ,Y_(s) and integer parameters p₁, p₂, . . . , p_(s) and outputting apseudo-random number sequence of length N.
 8. A receiver comprising; asignal receiving section that receives a signal; an output unit of anyof claims 1 to 4 that outputs a pseudo-random number sequence of lengthN; an inverse spreading section that uses the output pseudo-randomnumber sequence of length N as a spreading code to inverselyspectrum-spread the received signal; and an output section that outputsthe inversely spectrum-spread signal as a signal for transmission. 9.The receiver according to claim 8, further comprising: a selectingsection that selects sequence initial values Y₁, Y₂, . . . , Y_(s) andinteger parameters p₁, p₂, . . . , p_(s); and a parameter transmittingsection that transmits the selected sequence initial values Y₁, Y₂, . .. , Y_(s) and integer parameters p₁, p₂, . . . , p_(s); the output unitaccepting input of the selected sequence initial values Y₁, Y₂, . . . ,Y_(s) and integer parameters p₁, p₂, . . . , p_(s) and outputting apseudo-random number sequence of length N.
 10. The receiver according toclaim 8, further comprising: a parameter receiving section that receivessequence initial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁,p₂, . . . , p_(s); the output unit accepting input of the receivedsequence initial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁,p₂, . . . , p_(s) and outputting a pseudo-random number sequence oflength N.
 11. A communication system comprising: the transmitter ofclaim 6; and the receiver of claim 10; the receiver receiving sequenceinitial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . .. , p_(s) transmitted by the transmitter; and the receiver alsoreceiving a signal transmitted by the transmitter.
 12. A communicationsystem comprising: the transmitter of claim 7; and the receiver of claim9; the transmitter receiving sequence initial values Y₁, Y₂, . . . ,Y_(s) and integer parameters p₁, p₂, . . . , p_(s) transmitted by thereceiver; and the receiver receiving a signal transmitted by thetransmitter.
 13. A filter unit for filtering a prescribed real impulseconstant r (−1<r<1), the filter unit comprising: an input terminal thataccepts input of an input signal of chip length D; a delay section thatoutputs a plurality of signals produced by delaying the input signalwhose input was accepted by 0, D, 2D, 3D, . . . , (N−1)D; an amplifyingsection that amplifies the delayed output signals (−r)^((N-T)/D) times,where T is the delay time, and outputs the amplified signals; an addersection that sums the output amplified signals and outputs the resultingsum signal; and an output terminal that outputs the output sum signal.14. The filter according to claim 13, wherein one or more of the delaysection, amplifying section and adder section of the filter unit areconstituted as an ASIC (Application Specific Integrated Circuit), a DSP(Digital Signal Processor) or an FPGA (Field Programmable Gate Array).15. A pseudo-random number sequence output method that is responsive tos (1≦s) number of prescribed positive integers q₁, q₂, . . . , q_(s), aprescribed real impulse constant r (−1<r<1), and a prescribed non-zeroreal constant C for outputting a pseudo-random number sequence of lengthN (1≦N), which output method comprises: an input acceptance step thataccepts s (1≦s) number of real number sequence initial values Y₁, Y₂, .. . , Y_(s) (−1<Y₁<1, −1<Y₂<1, . . . , −1 Y_(s)<1), and s number ofinteger parameters p₁, p₂, . . . , p_(s) (2≦p₁, 2≦p₂, . . . 2≦p_(s)) forwhich q₁ mod p₁≠0, q₂mod p₂≠0. . . , q_(s) mod p_(s)≠0 respectively holdwith respect to the prescribed positive integers q₁, q₂. . . q_(s); acalculation step that uses the prescribed real impulse constant r, theprescribed non-zero real constant C, the sequence initial values Y₁, Y₂,. . . , Y_(s), the integer parameters p₁, p₂, . . . , p_(s), theprescribed positive integers q₁, q₂, . . . , q_(s) and integers j(1≦j≦s), m (1≦m≦2N−2) and n (1≦n≦2N−1) to calculate from the recurrenceformula T _(p)(cos θ)=T(p, cos θ)−cos(pθ) y _(j)[1]=Y _(j) y _(j)[m+1]=T(p _(j) ,y _(j) [m])${z\lbrack n\rbrack} = {\prod\limits_{j = 1}^{s}{T\left( {q_{j},{y_{j}\lbrack n\rbrack}} \right)}}$

a pseudo-random number sequence z′[1], z′[2], . . . , z′[N] of length Nthat satisfies $\begin{matrix}{{{z^{\prime}\lbrack 1\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\lbrack j\rbrack}}}}},} \\{{{z^{\prime}\lbrack 2\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\left\lbrack {j + 1} \right\rbrack}}}}},} \\\vdots \\{{{{z^{\prime}\lbrack N\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\left\lbrack {j + N - 1} \right\rbrack}}}}};}\quad}\end{matrix}$

an output step that outputs the pseudo-random number sequence z′[1],z′[2], . . . z′[N].
 16. The output method according to the presentinvention according to claim 15, wherein the sequence initial values Y₁,Y₂, . . . , Y_(s) satisfy y _(k)[2]T(p _(k) ,Y _(k)) y _(k) [m+1]T(p_(k) ,y _(k) [m]) Y _(k) =y _(k) [N+1]T(p _(k) ,y _(k) [N]) with respectto an integer k (1≦k≦s) and an integer m (1≦m≦N).
 17. The output methodaccording to claim 15 or 16, wherein the prescribed real impulseconstant r satisfies 2−{square root}{square root over (3)}−0.1≦r≦2−{square root}{square root over (3)}+0.1.
 18. The output methodaccording to any of claims 15 to 17, wherein every prescribed positiveinteger q₁, q₂. . . q_(s) is
 1. 19. A transmission method comprising: aninput acceptance step that accepts input of a signal for transmission;an output step that outputs a pseudo-random number sequence of length Nby the output method of any of claims 15 to 18; a spreading step thatuses the output pseudo-random number sequence of length N as a spreadingcode to spectrum-spread the signal for transmission whose input wasaccepted; and a signal transmitting step that transmits thespectrum-spread signal.
 20. The transmission method according to claim19, further comprising: a selecting step that selects sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . ,p_(s); and a parameter transmitting step that transmits the selectedsequence initial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁,p₂, . . . , p_(s); the output step accepting input of the selectedsequence initial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁,p₂, . . . , p_(s) and outputting a pseudo-random number sequence oflength N.
 21. The transmission method according to claim 19, furthercomprising: a parameter receiving step that receives sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . ,p_(s); the output step accepting input of the received sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . ,p_(s) and outputting a pseudo-random number sequence of length N.
 22. Areceiving method comprising; a signal receiving step that receives asignal; an output step that outputs a pseudo-random number sequence oflength N by the output method of any of claims 15 to 18; an inversespreading step that uses the output pseudo-random number sequence oflength N as a spreading code to inversely spectrum-spread the receivedsignal; and an output step that outputs the inversely spectrum-spreadsignal as a signal for transmission.
 23. The receiving method accordingto claim 22, further comprising: a selecting step that selects sequenceinitial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . .. , p_(s); and a parameter transmitting step that transmits the selectedsequence initial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁,p₂, . . . , p_(s); the output step accepting input of the selectedsequence initial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁,p₂, . . . , p_(s) and outputting a pseudo-random number sequence oflength N.
 24. The receiving method according to claim 22, furthercomprising: a parameter receiving step that receives sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . ,p_(s); the output step accepting input of the received sequence initialvalues Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . ,p_(s) and outputting a pseudo-random number sequence of length N.
 25. Afiltering method for filtering a prescribed real impulse constant r(−1<r<1 ), the filtering method comprising: an input step that acceptsinput of an input signal of chip length D; a delaying step that outputsa plurality of signals produced by delaying the input signal whose inputwas accepted by 0, D, 2D, 3D, . . . , (N−1)D; an amplifying step thatamplifies the delayed output signals (−r)^((N−T)/D) times, where T isthe delay time, and outputs the amplified signals; a summing step thatsums the output amplified signals and outputs the resulting sum signal;and an output step that outputs the output sum signal.
 26. Acomputer-readable data recording medium recorded with a program thatenables a computer to function as an output unit output unit responsiveto s (1≦s) number of prescribed positive integers q₁, q₂, . . . , q_(s),a prescribed real impulse constant r (−1<r<1), and a prescribed non-zeroreal constant C for outputting a pseudo-random number sequence of lengthN (1≦N), which output unit comprises: sequence initial values Y₁, Y₂, .. . , Y_(s) (−1<Y₁<1, −1<Y₂<1, . . . , −1 Y_(s)<1), and s number ofinteger parameters p₁, p₂, . . . , p_(s) (2≦p₁, 2≦p₂, . . . 2≦p_(s)) forwhich q₁ mod p₁≠0, q₂ mod p₂≠0. . . , q_(s) mod p_(s)≠0 respectivelyhold with respect to the prescribed positive integers q₁, q₂. . . q_(s);a calculation section that uses the prescribed real impulse constant r,the prescribed non-zero real constant C, the sequence initial values Y₁,Y₂, . . . , Y_(s), the integer parameters p₁, p₂, . . . , p_(s), theprescribed positive integers q₁, q₂, . . . , q_(s) and integers j(1≦j≦s), m (1≦m≦2N−2) and n (1≦n≦2N−1) to calculate from the recurrenceformula T _(p)(cos θ)=T(p, cos θ)−cos(pθ) y _(j) [1 ]=Y _(j) y _(j)[m+1]=T(p _(j) ,y _(j) [m])${z\lbrack n\rbrack} = {\prod\limits_{j = 1}^{s}{T\left( {q_{j},{y_{j}\lbrack n\rbrack}} \right)}}$

a pseudo-random number sequence z′[1], z′[2], . . . , z′[N] of length Nthat satisfies $\begin{matrix}{{{z^{\prime}\lbrack 1\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\lbrack j\rbrack}}}}},} \\{{{z^{\prime}\lbrack 2\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\left\lbrack {j + 1} \right\rbrack}}}}},} \\\vdots \\{{{{z^{\prime}\lbrack N\rbrack} = \quad {C{\sum\limits_{j = 1}^{N}{\left( {- r} \right)^{j}{z\left\lbrack {j + N - 1} \right\rbrack}}}}};}\quad}\end{matrix}$

an output section that outputs the pseudo-random number sequence z′[1],z′[2], . . . , z′[N].
 27. The data recording medium according to claim26, whose program operates the computer to function so that the sequenceinitial values Y₁, Y₂, . . . , Y_(s) satisfy y _(k)[2]T(p _(k) ,Y _(k))y _(k) [m+1]T(p _(k) ,y _(k) [m]) Y _(k) =y _(k) [N+1]T(p _(k) ,y _(k)[N]) with respect to an integer k (1≦k≦s) and an integer m (1≦m≦N). 28.The data recording medium according to claims 26 or 27, whose programoperates the computer to function so that the prescribed real impulseconstant r satisfies 2−{square root}{square root over(3)}−0.1≦r≦2−{square root}{square root over (3)}+0.1.
 29. The datarecording medium according to any of claims 26 to 28, whose programoperates the computer to function so that every prescribed positiveinteger q₁, q₂. . . q_(s) is
 1. 30. A compute,-readable data recordingmedium recorded with a program that enables a computer to function as atransmitter comprising: an input acceptance section that accepts asignal for transmission; an output unit of any of claims 1 to 4 thatoutputs a pseudo-random number sequence of length N; a spreading sectionthat uses the output pseudo-random number sequence of length N as aspreading code to spectrum-spread the signal for transmission whoseinput was accepted; and a signal transmitting section that transmits thespectrum-spread signal.
 31. The data recording medium according to claim30, whose program further operates the computer to function as: aselecting section that selects sequence initial values Y₁, Y₂, . . . ,Y_(s) and integer parameters p₁, p₂, . . . , p_(s); and a parametertransmitting section that transmits the selected sequence initial valuesY₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . , p_(s); andoperates the output unit to accept input of the selected sequenceinitial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . .. , p_(s) and output a pseudo-random number sequence of length N. 32.The data recording medium according to claim 30, whose program furtheroperates the computer to function as: a parameter receiving section thatreceives sequence initial values Y₁, Y₂, . . . , Y_(s) and integerparameters p₁, p₂, . . . , p_(s); and operates the output unit to acceptinput of the received sequence initial values Y₁, Y₂, . . . , Y_(s) andinteger parameters p₁, p₂, . . . , p_(s) and output a pseudo-randomnumber sequence of length N.
 33. A computer-readable data recordingmedium recorded with a program that enables a computer to function as areceiver comprising: a signal receiving section that receives a signal;an output unit of any of claims 1 to 4 that outputs a pseudo-randomnumber sequence of length N; an inverse spreading section that uses theoutput pseudo-random number sequence of length N as a spreading code toinversely spectrum-spread the received signal; and an output sectionthat outputs the inversely spectrum-spread signal as a signal fortransmission.
 34. The data recording medium according to claim 33, whoseprogram further operates the computer to function as: a selectingsection that selects sequence initial values Y₁, Y₂, . . . , Y_(s) andinteger parameters p₁, p₂, . . . , p_(s); and a parameter transmittingsection that transmits the selected sequence initial values Y₁, Y₂, . .. , Y_(s) and integer parameters p₁, p₂, . . . , p_(s); and operates theoutput unit to accept input of the selected sequence initial values Y₁,Y₂, . . . , Y_(s) and integer parameters p₁, p₂, . . . , p_(s) andoutput a pseudo-random number sequence of length N.
 35. The datarecording medium according to claim 33, whose program further operatesthe computer to function as: a parameter receiving section that receivessequence initial values Y₁, Y₂, . . . , Y_(s) and integer parameters p₁,p₂, . . . , p_(s); and operates the output unit to accept input of thereceived sequence initial values Y₁, Y₂, . . . , Y_(s) and integerparameters p₁, p₂, . . . , p_(s) and output a pseudo-random numbersequence of length N.
 36. A computer-readable data recording mediumrecorded with a program that enables any of a computer, DSP (DigitalSignal Processor) and FPGA (Field Programmable Gate Array) to functionas filter unit for filtering a prescribed real impulse constant r(−1<r<1), the filter unit comprising: an input terminal that acceptsinput of an input signal of chip length D; a delay section that outputsa plurality of signals produced by delaying the input signal whose inputwas accepted by 0, D, 2D, 3D, . . . , (N−1)D; an amplifying section thatamplifies the delayed output signals (−r)^((N−T)/D) times, where T isthe delay time, and outputs the amplified signals; an adder section thatsums the output amplified signals and outputs the resulting sum signal;and an output terminal that outputs the output sum signal.
 37. A datarecording medium according to any of claims 26 to 36, wherein the datarecording medium is a compact disk, floppy disk, hard disk,magneto-optical disk, digital video disk, magnetic tape, orsemiconductor memory.